Vertex Representations for Yangians of Kac-Moody algebras

Curtis Wendlandt; Nicolas Guay; Vidas Regelskis

Vertex Representations for Yangians of Kac-Moody algebras

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arxiv 1804.04081 v2 pith:SZXQUYW2 submitted 2018-04-11 math.RT math.QA

Nicolas Guay , Vidas Regelskis , Curtis Wendlandt This is my paper · ORCID

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keywords kac-moodylacedrepresentationssimplyvertexyangiansaffinealgebra

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Using vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.

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Level one Weyl modules for toroidal Lie algebras
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The level-one global Weyl module of a toroidal Lie algebra is isomorphic to an S^{-1}-twist of a known vertex-operator module, giving closed character formulas.

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